Dear Colleagues,

We continue our Colloquium in the Math Department.

Sergei Avdonin,

Dept. of Mathematical Sciences,

University of Alaska Fairbanks

Thursday, March 18 , EMCS 239, 3:00pm.

Control and Inverse Problems for the Wave equation on Graphs

Abstract

Differential equations on graphs are used to describe many physical
processes such as mechanical vibrations of multi-linked flexible
structures usually composed of flexible beams or strings, propagation of
electro-magnetic waves in networks of optical fibers, heat flow in
multi-link networks, and also electron flow in quantum mechanical
circuits. In this talk we describe new controllability results for the
wave equation on graphs without cycles. We prove exact boundary
controllability of such systems and find a sharp estimate of
controllability time. Basing on these results we solve the inverse
(identification) problem --- recover the topology of the graph and
density of the strings using boundary observations. We discuss how our
results can be applied for solving control and inverse problems for the
heat and
Schr\"odinger equations.

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Boris P Belinskiy

Department of Mathematics, Dept. 6956

University of Tennessee at Chattanooga

Ph. (423) 425-4748